A RISK-SENSITIVE STOCHASTIC MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL OF JUMP DIFFUSIONS AND ITS APPLICATIONS

A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.

Risk-sensitive reinforcement learning algorithms with generalized average criterion

A new algorithm is proposed, which immolates the optimality of control policies potentially to obtain the robnsticity of solutions. The robnsticity of solutions maybe becomes a very important property for a learning system when there exists non-matching between theory models and practical physical system, or the practical system is not static, or the availability of a control action changes along with the variety of time. The main contribution is that a set of approximation algorithms and their convergence results are given. A generalized average operator instead of the general optimal operator max （or rain） is applied to study a class of important learning algorithms, dynamic prOgramming algorithms, and discuss their convergences from theoretic point of view. The purpose for this research is to improve the robnsticity of reinforcement learning algorithms theoretically.

Optimal Risk-Sensitive Filtering for System Stochastic of Second and Third Degree

The risk-sensitive filtering design problem with respect to the exponential mean-square cost criterion is con-sidered for stochastic Gaussian systems with polynomial of second and third degree drift terms and intensity parameters multiplying diffusion terms in the state and observations equations. The closed-form optimal fil-tering equations are obtained using quadratic value functions as solutions to the corresponding Focker- Plank-Kolmogorov equation. The performance of the obtained risk-sensitive filtering equations for stochastic polynomial systems of second and third degree is verified in a numerical example against the optimal po-lynomial filtering equations (and extended Kalman-Bucy for system polynomial of second degree), through comparing the exponential mean-square cost criterion values. The simulation results reveal strong advan-tages in favor of the designed risk-sensitive equations for some values of the intensity parameters.

Partially Observed Risk-Sensitive Stochastic Control Problems with Non-Convexity Restriction

The paper considers partially observed optimal control problems for risk-sensitive stochastic systems,where the control domain is non-convex and the diffusion term contains the control v.Utilizing Girsanov’s theorem,spike variational technique as well as duality method,the authors obtain four adjoint equations and establish a maximum principle under partial information.As an application,an example is presented to demonstrate the result.

G-stochastic maximum principle for risk-sensitive control problem and its applications

This study advances the G-stochastic maximum principle(G-SMP)from a risk-neutral framework to a risk-sensitive one.A salient feature of this advancement is its applicability to systems governed by stochastic differential equations under G-Brownian motion(G-SDEs),where the control variable may influence all terms.We aim to generalize our findings from a risk-neutral context to a risk-sensitive performance cost.Initially,we introduced an auxiliary process to address risk-sensitive performance costs within the G-expectation framework.Subsequently,we established and validated the correlation between the G-expected exponential utility and the G-quadratic backward stochastic differential equation.Furthermore,we simplified the G-adjoint process from a dual-component structure to a singular component.Moreover,we explained the necessary optimality conditions for this model by considering a convex set of admissible controls.To describe the main findings,we present two examples:the first addresses the linear-quadratic problem and the second examines a Merton-type problem characterized by power utility.

Design of satisfaction output feedback controls for stochastic nonlinear systems under quadratic tracking risk-sensitive index

In this paper, the design problem of satisfaction output feedback controls for stochastic nonlinear systems in strict feedback form under long-term tracking risk-sensitive index is investigated. The index function adopted here is of quadratic form usually encountered in practice, rather than of quartic one used to beg the essential difficulty on controller design and performance analysis of the closed-loop systems. For any given risk-sensitive parameter and desired index value, by using the integrator backstepping method, an output feedback control is constructively designed so that the closed-loop system is bounded in probability and the risk-sensitive index is upper bounded by the desired value.

Quasi-equality constrained risk-sensitive filtering for nonlinear discrete-time systems

More and more data fusion models contain state constraints with valuable information in the filtering process. In this study, an optimal filter of risk sensitive with quasi-equality constraints is formulated using the reference probability method. Through recursion processes of probability density acquired from the probability measure change, the derived algorithm is optimal in the sense of the risk sensitive parameter. The system and constraint models are Consistent in statistics. Simulation results show that it is more robust and efficient than projection filters for the worst-case of noises and model uncertainty.

Stressed portfolio optimization with semiparametric method

Tail risk is a classic topic in stressed portfolio optimization to treat unprecedented risks,while the traditional mean–variance approach may fail to perform well.This study proposes an innovative semiparametric method consisting of two modeling components:the nonparametric estimation and copula method for each marginal distribution of the portfolio and their joint distribution,respectively.We then focus on the optimal weights of the stressed portfolio and its optimal scale beyond the Gaussian restriction.Empirical studies include statistical estimation for the semiparametric method,risk measure minimization for optimal weights,and value measure maximization for the optimal scale to enlarge the investment.From the outputs of short-term and long-term data analysis,optimal stressed portfolios demonstrate the advantages of model flexibility to account for tail risk over the traditional mean–variance method.

Robust Designs Through Risk Sensitivity:An Overview

This is an overview paper on the relationship between risk-averse designs based on exponential loss functions with or without an additional unknown(adversarial)term and some classes of stochastic games.In particular,the paper discusses the equivalences between risk-averse controller and filter designs and saddle-point solutions of some corresponding risk-neutral stochastic differential games with different information structures for the players.One of the by-products of these analyses is that risk-averse controllers and filters(or estimators)for control and signal-measurement models are robust,through stochastic dissipation inequalities,to unmodeled perturbations in controlled system dynamics as well as signal and the measurement processes.The paper also discusses equivalences between risk-sensitive stochastic zero-sum differential games and some corresponding risk-neutral three-player stochastic zero-sum differential games,as well as robustness issues in stochastic nonzero-sum differential games with finite and infinite populations of players,with the latter belonging to the domain of mean-field games.